Filters and duplexers employed in mobile phones are desired to have low insertion loss and high suppression characteristics. The reason why low insertion loss is desired is as follow. In a case of a transmit filter, as the insertion loss decreases, the electrical power consumption of the mobile phone is reduced, and thus, battery run time can be increased. In a case of a receive filter, as the insertion loss decreases, the S/N (signal/noise) ratio of a reception signal is improved, and the receiving sensitivity and the communication quality of the mobile phone can be improved. Therefore, the insertion loss of the filter is desired to be as small as possible. Ladder-type filters and double-mode filters using an acoustic wave resonator are used as filters employed in mobile phones.
Surface acoustic wave resonators, boundary acoustic wave resonators, and Love wave resonators including an IDT (Interdigital Transducer) have been used as the acoustic wave resonator. The IDT includes two comb-shaped electrodes facing each other on a piezoelectric substrate. Japanese Patent Application Publication Nos. 2004-537235 and 2013-12883 disclose modulating a gap position between an electrode finger and a dummy electrode finger in the IDT. A Rayleigh wave scattering in a surface acoustic wave resonator is described in IEEE Trans. Ultrason. Ferroelect., Freq. Contr., Vol. 48, no. 6, pp. 1517-1526, 2001 (Non Patent Document 1).
In a filter using a resonator including an IDT, loss in the passband and the degree of suppression outside the passband are in a trade-off relationship. That is to say, when the loss in the passband is designed to be small, the suppression outside the passband deteriorates. As described above, it is difficult to reduce the loss in the passband without deteriorating the degree of suppression outside the passband. The loss in the passband of the filter can be reduced by improving the Q value of a resonator in the filter.